Eligible patients will begin with a 14 day lead-in period with afatinib alone. This will be followed immediately by 2 cycles of induction chemotherapy with carboplatin AUC 6 IV, paclitaxel 175mg/m2 day 1, and afatinib as a continuous daily dosing. Each cycle is repeated every 21 days. All patients will receive concurrent chemoradiotherapy beginning 2-3 weeks after the completion of the second cycle of induction chemotherapy (Refer to Study Schema in page 8 of the protocol).